Varimax rotation
Varimax rotation is a change of coordinates used in principal component analysis that maximizes the sum of the variance of the loading vectors. That is, it seeks a basis such that most economically represents each individual—that each individual can be well described by a linear combination of only a few basis functions. Suggested by Henry Felix Kaiser in 1958, it is a popular scheme for orthogonal rotation which cleans up the factors as follows: "for each factor, high loadings (correlations) will result for a few variables; the rest will be near zero." The advantages and disadvantages of the technique is discussed at the website of Columbia University . Varimax rotation in personality research See also * Empirical orthogonal functions * Equimax rotation * Multivariate analysis * Q methodology * Rotation matrix * Statistical rotation References Further reading Books *Lee, H. B. (1979). An empirical comparison of some factor analytic methods. Lee, Howard B : U California, Los Angeles. *Newton, B. E. (2001). A critical study of the varimax rotation method, with a comparison to Bieber's invariance solution for one-sample. Newton, Brian Edward: U Wyoming, US. Paper Adachi, K. (2004). Oblique Promax Rotation Applied to the Solutions in Multiple Correspondence Analysis. Behaviormetrika, 31(1), 1-12. *Agrawal, K. (1973). The meaning of work: IV. Reinterpreting factor structure. Journal of Psychological Researches, 17(1), 10-12. *Aiken, L. S. (1972). Simultaneous processing of typal and dimensional variation among multidimensional events. Multivariate Behavioral Research Vol 7(3) Jul 1972, 305-316. *Archer, C. O., & Jennrich, R. I. (1973). Standard errors for rotated factor loadings. Psychometrika, 38(4, 581-592. *Bhushan, V. (1978). A factor analysis of the Minnesota Teacher Attitude Inventory. Scientia Paedagogica Experimentalis, 15(2), 207-214. *Bianchi, G. (1973). Patterns of hypochondriasis: A principal components analysis. British Journal of Psychiatry Vol 122(570) May 1973, 541-548. *Bienvenu, M. J., & Stewart, D. W. (1976). Dimensions of interpersonal communication. Journal of Psychology: Interdisciplinary and Applied, 93(1), 105-111. *Boente, G., Pires, A. M., & Rodrigues, I. M. (2006). General projection-pursuit estimators for the common principal components model: Influence functions and Monte Carlo study. Journal of Multivariate Analysis, 97(1), 124-147. *Brand, C., & Egan, V. (1989). The "Big Five" dimensions of personality? Evidence from ipsative, adjectival self-attributions. Personality and Individual Differences, 10(11), 1165-1171. *Brems, C., & Johnson, M. E. (1990). Reexamination of the Bem Sex-Role Inventory: The interpersonal BSRI. Journal of Personality Assessment, 55(3-4), 484-498. *Carlson, R. W. (1979). Dimensionality of the Repression Sensitization Scale. Journal of Clinical Psychology, 35(1), 78-84. *Conger, A. J., Conger, J. C., Farrell, A. D., & Ward, D. (1979). What can the WISC-R measure? Applied Psychological Measurement, 3(4), 421-436. *Cureton, E. E., & Mulaik, S. A. (1975). The weighted varimax rotation and the promax rotation. Psychometrika, 40(2), 183-195. *Devoid, G. H. (2007). The motivations of online learners. Devoid, Gail Harrigan: Capella U , US. *Fowler, P. C. (1981). Maximum likelihood factor structure of the Family Environment Scale. Journal of Clinical Psychology, 37(1), 160-164. *Green, D. E., & Walkey, F. H. (1991). A fourth-order analysis of the Eysenck Personality Inventory: Some predictable results from an unusual analysis. Social Behavior and Personality, 19(3), 157-163. *Guilford, J. (1977). The invariance problem in factor analysis. Educational and Psychological Measurement, 37(1), 11-19. *Gurel, L. (1967). Dimensions of Psychiatric Patient Ward Behavior. Journal of Consulting Psychology, 31(3), 328-331. *Harris, S. M., & Halpin, G. (2002). Development and validation of the Factors Influencing Pursuit of Higher Education Questionnaire. Educational and Psychological Measurement, 62(1), 79-96. *Hobi, V., & Klar, A. (1973). A combined factor analysis of the MMPI, FPI and 16-PF. Zeitschrift fur Klinische Psychologie, 1(2), 27-48. *Holmstrom, R. W., Karp, S. A., & Silber, D. E. (1992). Factor structure of the Apperceptive Personality Test (APT). Journal of Clinical Psychology, 48(2), 207-210. *Hull, J. T. (1980). Environmental normalization: A factor analysis. Psychosocial Rehabilitation Journal, 4(1), 20-26. *Huntingford, F. A. (1976). An investigation of the territorial behaviour of the three-spined stickleback (Gasterosteus aculeatus) using principal components analysis. Animal Behaviour, 24(4), 822-834. *Ibanez Guerra, E., Morales Meseguer, J. M., & Seoane Rey, J. (1975). Factorial structure of anxiety: Normal and neurotic anxiety. Archivos de Neurobiologia, 38(6), 519-530. *John, E., & et al. (1973). Factor analysis of evoked potentials. Electroencephalography & Clinical Neurophysiology Vol 34(1) Jan 1973, 33-43. *Kaemmerer, W. F., & Schwebel, A. I. (1976). Factors of the Rotter Internal-External Scale. Psychological Reports, 39(1), 107-114. *Kaiser, H. F., & Cerny, B. A. (1978). Casey's Method for fitting hyperplanes from an intermediate orthomax solution. Multivariate Behavioral Research, 13(4), 395-401. *Kiers, H. A. (1997). Three-mode orthomax rotation. Psychometrika, 62(4), 579-598. *Kiers, H. A. (1998). Joint orthomax rotation of the core and component matrices resulting from three-mode principal components analysis. Journal of Classification, 15(2), 245-263. *Kuramoto, H., Kanbayashi, Y., Nakata, Y., Fukui, T., Mukai, T., & Negishi, Y. (2002). Standardization of The Japanese Version of The Youth Self Report (YSR). Japanese Journal of Child and Adolescent Psychiatry, 43(Suppl), 17-32. *Michael, J. J., Devaney, R. L., & Michael, W. B. (1980). The factorial validity of the Cornell Critical Thinking Test for a junior high school sample. Educational and Psychological Measurement, 40(2), 437-450. *Mocks, J., & Verleger, R. (1986). Principal component analysis of event-related potentials: A note on misallocation of variance. Electroencephalography & Clinical Neurophysiology: Evoked Potentials, 65(5), 393-398. *Monk, T. H., & Kupfer, D. J. (2007). Which aspects of morningness-eveningness change with age? Journal of Biological Rhythms, 22(3), 278-280. *Morris, J. D. (1977). Rotating a discriminant analysis solution. Behavior Research Methods & Instrumentation, 9(1), 29. *Neudecker, H. (1981). On the matrix formulation of Kaiser's varimax criterion. Psychometrika, 46(3), 343-345. *Nevels, K. (1986). A direct solution for pairwise rotations in Kaiser's varimax method. Psychometrika, 51(2), 327-329. *Peltzer, K. (2002). Factor structure of religious problem-coping styles in an African sample. Social Behavior and Personality, 30(5), 509-514. *Pino, M., Dominguez, J., & Lopez-Castedo, A. (2007). Evaluating appreciation of measures attending to pupil diversity (EMAD). Psychological Reports, 100(3, Pt 1), 783-786. *Platten, M. R., & Williams, L. R. (1979). A comparative analysis of the factorial structures of two administrations of the Piers-Harris Children's Self Concept Scale to one group of elementary school children. Educational and Psychological Measurement, 39(2), 471-478. *Powers, S. (1984). PCOM: A microcomputer program that performs a principal components analysis. Educational and Psychological Measurement, 44(3), 679-680. *Puhan, B. N. (1981). Effects of marker variables on WAIS communalities. Educational and Psychological Measurement, 41(1), 55-59. *Rosler, F., & Manzey, D. (1981). Principal components and VARIMAX-rotated components in event-related potential research: Some remarks on their interpretations. Biological Psychology Vol 13 Dec 1981, 3-26. *Sawicki, R. F., & Golden, C. J. (1984). Multivariate statistical techniques in neuropsychology: I. Comparison of orthogonal rotation methods with the Receptive scale of the Luria-Nebraska Neuropsychological Battery. International Journal of Clinical Neuropsychology, 6(2), 126-134. *Stevenson, J. (1993). Multivariate statistics: V. The use of factor scores in psychiatric research. Nordic Journal of Psychiatry, 47(3), 169-178. *Stewart, R. A. (1974). Factor analysis and rotation of the 566 MMPI items. Social Behavior and Personality, 2(2), 147-156. *Stewart, R. A. (1977). Factor analysis and rotation of responses to the Junior Eysenck Personality Inventory. Psychological Reports, 40(2), 599-601. *Taysi, E. (2007). Transgression-Related Interpersonal Motivations Inventory: A study of validity and reliability. Turk Psikoloji Yazilari, 10(20), 63-74. *ten Berge, J. M. (1984). A joint treatment of varimax rotation and the problem of diagonalizing symmetric matrices simultaneously in the least-squares sense. Psychometrika, 49(3), 347-358. *Vegelius, J., & Backstrom, A. (1981). An enquiry about religion, analyzed by a nominal scale truncated component analysis. Educational and Psychological Measurement, 41(3), 717-724. *Veldman, D. J. (1974). Simple structure and the number of factors problem. Multivariate Behavioral Research Vol 9(2) Apr 1974, 191-200. *Wastell, D. (1981). PCA and VARIMAX rotation: Some comments on Rosler and Manzey. Biological Psychology Vol 13 Dec 1981, 27-29. *Wood, J. M., Tataryn, D. J., & Gorsuch, R. L. (1996). Effects of under- and overextraction on principal axis factor analysis with varimax rotation. Psychological Methods, 1(4), 354-365. External links * Factor rotations in Factor Analyses by Herve Abdi * About Varimax * Properties of Principal Components Category:Orthogonal rotation